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<p>In this paper, we study the sets of integers which are <i>n</i>-th terms of Lucas sequences. We establish lower- and upper bounds for the size of these sets. These bounds are sharp for <i>n</i> sufficiently large. We also develop bounds on the growth order of the terms of Lucas sequences that are independent of the parameters of the sequence, which is a new feature.</p>

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Integers represented by Lucas sequences

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月19日

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  • Lajos Hajdu,
  • Rob Tijdeman

摘要

In this paper, we study the sets of integers which are n-th terms of Lucas sequences. We establish lower- and upper bounds for the size of these sets. These bounds are sharp for n sufficiently large. We also develop bounds on the growth order of the terms of Lucas sequences that are independent of the parameters of the sequence, which is a new feature.